This invention relates generally to nuclear magnetic resonance imaging (MRI), and more particularly the invention relates to motion analysis and imaging of an organ such as the heart or a system such as the musculoskeletal system using phase contrast MRI maps of tissue velocity in the organ.
MRI methods that produce images whose intensity is proportional to velocity generally belong to the class called phase contrast MRI. Phase contrast principles have been combined with the cine imaging methods to enable the production of images that portray the distribution of velocities at multiple points in the cardiac cycle. See, Pelc et al., Magnetic Resonance Quarterly, Vol. 7, No. 4, 1991, pp. 229-254.
Pelc, U.S. Pat. No. 5,195,525, discloses apparatus and a method for analyzing the motion of specific regions using phase contrast cine data. Basically, the phase contrast MRI technique provides maps of vector velocity in the object through the motion cycle. In the technique described in the '525 patent, the operator selects a region to be tracked by identifying its location in the first frame of the cine image set. The velocity in the region in the first frame is used to calculate its expected location in the second frame. The vector velocity in the second frame at the new location as portrayed in the cine set is used to calculate the position in the third frame, and so on. This tracking can be performed in three dimensions and promises to yield important information about cardiac motion noninvasively. Higher order integration methods can be used to improve the motion estimate.
The '525 patent explains how the motion of a small region can be calculated by integrating the measured velocity data. Copending Pelc application Ser. No. 07/865,437, filed Apr. 9, 1992, now U.S. Pat. No. 5,257,625 explains that if the motion is known to be periodic, this a priori information can be used to advantage. Specifically, the region must return to its starting location at the end of the cycle. This knowledge can be used to improve the stability of the computed motion by iteratively finding the velocity offset that, when subtracted from all the measured velocities, minimizes the discrepancy between the starting and ending positions of the region (i.e., a forced closure). Copending Pelc et al. application Ser. No. 07/921,804, filed Jul. 28, 1992, now U.S. Pat. No. 5,257,626 exploits the that knowledge the motion is periodic in a different manner. Because of the cyclical nature of the motion, integration of the velocity field can be performed not only forward in time but also backward in time. In the backward integration, one computes, for each frame, the location from which the object has come. In this way, two trajectories (forward and backward) are computed. The '804 application shows that there is a preferred manner in which the two can be combined to produce a single estimated trajectory which has lower noise and decreased sensitivity to added velocity errors. Thus, the preferred algorithm for tracking the motion of a region uses forward and backward integration, computation of a combined trajectory, and iterative forced closure.
The '525 patent includes the concept of tracking a deformable region. In this approach, the region is allowed to translate, rotate and deform as it moves through the cycle. Allowing the region to deform is important since much of the information about the functioning of a muscle is obtained in this portion of the analysis, the strain tensor. As explained in the patent, whereas rigid translation is determined by the average velocity in the region at each point in time in the cycle, the information about rotation and deformation (strain) is contained in the spatial derivatives of the velocity field. To calculate rigid motion, one integrates the velocity field. To calculate rotation and strain as functions of time, one integrates the spatial gradients of the velocity field. The concepts of forced closure and bidirectional integration can be used within an algorithm that integrates rotation and deformation.
As is further explained in the '525 patent, one must maintain a consistent coordinate system if the strain information is to integrated properly. Thus, suppose that early in the cycle a region shortens in one direction. This direction, for example, may have something to do with the direction of muscle fibers within the region. Further, suppose that the region also rotates early in the cycle, and later in the cycle, continues to shorten in the direction of the fibers. The direction of shortening has rotated in the laboratory frame but not with respect to the fibers, the relevant frame of reference. Thus, the integration must be performed with respect to a consistent frame of reference. In the '525 patent, this is done by rotating the incremental strain tensor in each frame by the negative of the rotation up to that frame. Integration of the strain tensor is done on the rotated incremental strains.
The present invention is directed to a method and apparatus for tracking of deformable regions by phase contrast MRI which is simpler to implement than the prior art.